Question 125260
{{{Quadratic Regression}}} is a process by which the equation of a parabola of "{{{best fit}}}" is found for a {{{set}}}{{{ of}}}{{{ data}}}.

Example:

for a set of data

{{{x}}}    | {{{y}}}
1  |-8
-5 | 0
2  | 5


The quadratic regression is:

{{{y = a x^2 + b x +c}}}


where:	{{{a = 2.0476190476190474}}}
	{{{b = 6.857142857142857}}}
and	{{{c = -16.904761904761905}}}

The error is: {{{0.0}}}
	


for a set of data


{{{x}}}  | {{{y}}}
1  |-8
-5 | 0
2  | 5
0  | 0


The quadratic regression is {{{y = a x^2 + b x +c}}}

where:	{{{a = 0.5554968287526427}}}
	{{{b = 1.9519027484143765}}}
and	{{{c = -3.940274841437632}}}


The error is: {{{13.509513742071881}}}

	
Quadratic Regression on the TI-83

1. Press the Y= key and clear any equations.

2. Press the STAT key, use the arrow keys to select EDIT, and enter this data:

{{{L1}}}	|{{{L2}}}
1	|230
2	|310
3	|350
4	|360
5	|350
6	|300
7	|220



3. Press the STAT key, select CALC, and choose option number 5: QuadReg. This will bring you back to the home screen, with QuadReg showing. Type "L1, L2" by pressing 2nd and 1, then comma, then 2nd and 2. Type "Y1" by pressing VARS, move across to Y-VARS, choosing Function, and choosing option number 1. Your home screen should show:
QuadReg {{{L1}}}, {{{L2}}}, {{{Y1}}}

Now press ENTER. You will see something like results in examples above